Physics 9702 · AS & A Level · Equations of motion

Equations of motion — practice question

A steel ball is released from a platform on a tower and lands on the ground below, as shown in Fig. 3.1. It drops from rest through a vertical distance of $192\text{ m}$. The ball has mass $270\text{ g}$.
(a(i)(1))[2]

Assume air resistance is negligible. Calculate the time for the ball to reach the ground.

(a(i)(2))[2]

Assume air resistance is negligible. Calculate the ball’s maximum kinetic energy.

(a(ii))[1]

State and explain how the ball’s velocity changes with time as it falls to the ground.

(a(iii))[1]

Show that the ball’s speed on reaching the ground is about $60\text{ m s}^{-1}$.

(b(i))[3]

In real conditions, air resistance is not negligible. Use Fig. 3.2 to state and explain qualitatively how the ball’s acceleration varies with the distance it has fallen.

(b(ii))[2]

The ball’s speed becomes $40\text{ m s}^{-1}$. Calculate its acceleration at this speed.

(b(iii))[2]

Use information from (a)(iii) and Fig. 3.2 to state and explain whether or not the ball reaches terminal velocity.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies $s = ut + \tfrac{1}{2}at^2$ with $192 = \tfrac{1}{2} \times 9.81 \times t^2$, giving $t = 6.3\ (6.26)\ \mathrm{s}$

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